Christopher Nolan said it was important for the League of Shadows to return, so yes, they are the League of Shadows. The League were shown in the flashbacks in TDKR to be a bunch of gunmen. The gunmen in Batman Begins at the monastery wore the same red scarves that the League members wore in The Dark Knight Rises. Bruce Wayne was never supposed to be Ra's successor, he was supposed to be Ra's' right-hand man out in front in the attack on Gotham. That's what the movie says.

I guess it's how you look at it. Yes, they wore the same garb as the guys in BB, but it doesn't mean they are the real "LOS". Just like people were dressing up as "Batman" in TDK. Are they the real Batman? No.

So, I still don't think it's Ra's's LOS. I think it's more along the line of Bruce's actions have come back to haunt him. That is what I think Nolan means.

Finally, Ra's tells Bruce in at his birthday party he is so disappointed because Bruce was his "greatest student". So you're telling me that he wouldn't want Bruce to take over?

But if Nolan were to say that this was the same LOS as in BB, then I'm in the minority because I don't see many similarities. Also as I wrote in the post above, if Talia was in the real LOS, where was she during BB? This was the first plot hole I noticed and was one reason why I was hoping Talia was just a rumor. They should've left the LOS alone as Bruce defeated them in BB. Also, all Ra's says to Bruce is that "my wife and daughter were taken from me". They should've left it at that. Now we're confused as to what was going on with Talia when Ra's was training Bruce? We certainly know she wasn't going to ditch Bane as he was her "protector".

One more thing, in BB, the LOS does their thing behind the scenes. In TDKR, they are front in center. Too many differences, in my opinion.